论文标题
在半明确数量及其真实价值的滑轮上
On sheaves on semicartesian quantales and their truth values
论文作者
论文摘要
在本文中，我们介绍了针对半明确量化的束带的新定义，提供了第一个示例和分类属性。我们注意到，我们的绳索类似于区域上的捆的标准定义，但是，我们通常证明这不是基本的topos-因为外部真实值的晶格$ sh（q）$，$ sub（1）$，在典型上是量子上的量子质量等同词，以量子$ q $的一部分，将其作为较大的元素（不一定是莫尼尼德级别的一部分）。为了开始研究，我们正在介绍的带束带类别的逻辑方面，我们探讨了此类搁板类别中“内部真实价值对象”的性质。更确切地说，我们分析了两名候选者的亚对象分类器，用于交换性和半明确数量的不同亚类。
In this paper, we introduce a new definition of sheaves on semicartesian quantales, providing first examples and categorical properties. We note that our sheaves are similar to the standard definition of a sheaf on a locale, however, we prove in that in general it is not an elementary topos - since the lattice of external truth values of $Sh(Q)$, $Sub(1)$, is canonically isomorphic to the quantale $Q$ - placing this paper as part of a greater project towards a monoidal (not necessarily cartesian) closed version of elementary topos. To start the study the logical aspects of the category of sheaves we are introducing, we explore the nature of the "internal truth value objects" in such sheaves categories. More precisely, we analyze two candidates for subobject classifier for different subclasses of commutative and semicartesian quantales.
